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Universality of Correlation Functions of Hermitian Random Matrices in an External Field

Research paper by P. Zinn-Justin

Indexed on: 01 Jun '98Published on: 01 Jun '98Published in: Communications in Mathematical Physics



Abstract

The behavior of correlation functions is studied in a class of matrix models characterized by a measure exp(−S) containing a potential term and an external source term: S=N tr(V(M) −MA). In the large N limit, the short-distance behavior is found to be identical to the one obtained in previously studied matrix models, thus extending the universality of the level-spacing distribution. The calculation of correlation functions involves (finite N) determinant formulae, reducing the problem to the large N asymptotic analysis of a single kernel K. This is performed by an appropriate matrix integral formulation of K. Multi-matrix generalizations of these results are discussed.